A tomography machine may be used to pass a radiation beam through a body, (e.g., the body of a patient), from different projection angles. The radiation beam hits a detector surface of the tomography machine, where individual pixel sensors, one for each picture element or pixel of the detector surface, detect the radiation intensity. The pixel values of a projection or acquisition are brought together in an acquisition data set. An acquisition data set refers to a data set containing pixel values of pixels of a detector surface of a tomography machine, wherein each pixel value characterizes the effect of attenuation values of body elements of the body on a projection beam that has passed through the body elements successively at a defined acquisition time and has then hit the pixel of the detector surface.
A graphical 3D model of the body may be reconstructed from the acquisition data sets that were obtained from different projection angles. The 3D model may be obtained, for example, using the known algorithm of filtered back projection. In order for this 3D reconstruction to produce a sharp or clear image of body elements of the body, so for instance of internal organs, it is necessary that the position of the body does not change, (e.g., the body remains stationary), in order that the pixel values from different acquisition data sets may be assigned correctly to the image values of the object. Should the body move, then a correct assignment may still be made if the movement is known precisely (e.g., by an additional tracking system). If this information is not available, an image of the body regions in the 3D model is obtained that is blurred or impaired by overlaid stripes (e.g., originating from edges). The generic term “motion artifacts” is used here.
A method for detecting a movement of a body is known from EP 2 490 180 A1, which method uses two acquisition data sets as the basis for calculating in each case a derivative of a planar integral, which derivative is also referred to as an intermediate function. The planar integral constitutes the 3D Radon transform. The intermediate function value characterizes for a virtual sectional plane of the body, the total of all the attenuation values of the body elements of the body that are located in this sectional plane. The intermediate function value may be determined here on the basis of the first acquisition data set and also independently thereof on the basis of the second acquisition data set. If the body has moved between the acquisition times of the two projections, then the two intermediate function values will differ.
A method for correcting misalignment for imaging techniques is known from WO 2014/108237 A1. This method likewise uses the intermediate function to determine a difference between two acquisition data sets. This publication denotes the intermediate function by the function g3. In order to determine the geometric misalignment (caused by, e.g., incorrect calibration or displacement/twisting/deformation of the components) of the tomography machine between two acquisition times, a difference value d between the intermediate function values of two acquisition data sets is determined. To achieve robust detection of the misalignment, instead of determining just one single difference value d, a plurality of virtual sectional planes of the body are defined, and for each sectional plane, two intermediate function values are determined on the basis of two acquisition data sets, one value for each set, and one difference value d is in turn determined from these two values. The difference values d are combined to form a total error value D. The number of selected sectional planes may be chosen to be very high in this method, and is limited by the resolution and dimensions of the detector. In addition, the total error value D may be used as the basis for adjusting sequentially one geometry parameter of the tomography machine at a time in order to correct the geometric misalignment. This sequential adjustment may result in a sub-optimum correction result, because not all the geometry parameters are mutually independent. Thus, in some cases, a plurality of iterations may be needed (e.g., repeated optimization of the same geometry parameter).